and \({\rm d}s\)  is the infinitesimal arc length. In [1]}, [2]}, [3]} \(\mathcal {W}_{1}\)  is referred to as \({W}_2^{1,1}\) . It was shown in [1]}, [2]} that it is the only linearly independent translation invariant Minkowski tensor that contains extra information over its scalar counterpart. The extra information contained in \(\mathcal {W}_{1}\)  is that of anisotropy. Any anisotropy in the boundary curve will manifest as an inequality between the eigenvalues of the matrix \({\cal W}_{1}\) . We define the eigenvalues in ascending order, \(\lambda _1<\lambda _2\)  and define the shape anisotropy parameter as \(\beta \equiv \lambda _1/\lambda _2\) . Hence for a generic curve, \(\beta \)  will have values between 0 and 1. The CMT also gives an estimate of length of the enclosing curve, since \(\mathbf {Tr}\left(\mathcal {W}_{1}\right)\)  is the perimeter of the curve and related to the second scalar MF i.e. the total contour length denoted by \(W_1\) . If \(\lambda \equiv (\lambda _1+ \lambda _2)\)  denotes the perimeter of the closed curve and is equated to the circumference of a circle i.e. \(2\pi r\) , we define \(r\)  to be an effective radius:
\(r\equiv \lambda /2\pi .\) 
